Grunkle Stan's Pet the Dog moment. Considering what we've seen of his character so far, letting Dipper and Mabel each pick something from the Mystery Shack gift shop is a pretty big deal.
"This journal told me there was no one in Gravity Falls I could trust. But when you battle a hundred gnomes side by side with someone, you realize that they've probably always got your back."
The theme of trust between Dipper and Mabel that sets up their teamwork for the rest of the show is done really well, and also gives us a lot of really adorable sweet sibling moments. Considering this is the first episode, there are sure to be more.
Heck, the relationship between the twins in general counts. Sure, they pester each other a lot, but not five minutes go by when it's not clear they're the best of friends. And after so many Disney Channel shows where any siblings in the show are almost always at each others' necks with the sweet moments few and far between, the only exception being another animated show taking place in the summer, it's a real breath of fresh air.
In "The Legend of the Gobblewonker", after abandoning Grunkle Stan to go chase a monster that turned out to be just a very tech savvy hillbilly who explained that he wanted some attention from his family. Dipper and Mabel (and Soos) decide to go back and spend time with each other like poor Stan originally planned to.
Grunkle Stan affectionately noogie-ing Dipper and Mabel at the end of "Headhunters".
Mabel saving the soon-to-be-eaten lobster and keeps him as a pet.
Dipper helping Mabel out of Sweater Town in "The Hand That Rocks the Mabel", followed by him offering to break the news about her wanting to break up with Gideon for her so she wouldn't have to. That was seriously nice of him, even if it had unintended consequences.
The reason why Mabel is so enthusiastic about befriending Gideon at first is that she likes having someone to do girly things with, since Soos and Dipper do "boy things" all the time. How does the episode end? With Mabel bedazzling Soos.
Grunkle Stan, Dipper and Mabel bonding over their shared dislike for Lil' Gideon.
Wendy lying to her friends about how Dipper defeated the ghosts in "The Inconveniencing" so that he could keep whatever dignity he had left, even though she clearly loved his dance.
Wendy and Dipper's interactions in general are very sweet. Wendy is such a nice character in general - she hangs with friends her age and is a rowdy teen, alright, but she is NEVER conescending to the kids and treats both Mabel and Dipper as equals, goofing around with them when, really, she doesn't have to at all. That, and Dipper's crush on Wendy is in general kind of adorable and well portrayed, as also seen in "Double Dipper".
Wendy and Dipper "ganging up" on the video game ref in the beginning of Fight Fighters was oddly adorable before Robbie showed up, anyway.
In " Dipper vs. Manliness", after Dipper tells his story about the Manotaurs and the Multi-Bear, Grunkle Stan points out how doing the right thing in spite of the pressure is rather manly. Let me repeat, Grunkle Stan said this.
Dipper choosing not to kill the Multi-Bear, despite all the pressure to do so, simply because it wasn't the right thing to do.
It's a brief moment, but in the diner, Manly Dan can be seen with his daughter Wendy, eating pancakes with her. It lead to the interpretation that this is how Manly Dan bonds with his daughter: over breakfast. Even if her brothers weren't around, it was nice to see Manly Dan interact with Wendy.
In "Double Dipper", we have Mabel's new friends staying with her even though she lost the dance contest to Pacifica.
Also in "Double Dipper", Grunkle Stan cheers for Mabel and wanted her to win the contest. The other contestant wasn't the nicest regardless, but it goes to show that Grunkle Stan does care about Mabel.
Again, Dipper and Wendy have a fairly sweet moment. It's kind of downplayed, but their casual conversation when Dipper runs into her near the bathroom is just... nice.
Then there's the final scene with Dipper and Tyrone just talking together about what they've learned about not getting in their own way.
And Tyrone giving Dipper extra encouragement to go after Wendy as he melts away.
Earlier, Tyrone trying to feed Paper Jam Dipper. It's oddly heartwarming and funny and kind of creepy.
Dipper comforting Mabel after Pacifica treats her like crap in "Irrational Treasure", followed by a pep talk.
Dipper exposing the truth about Pacifica's family to her after her harsh treatment of Mabel, despite the fact that Mabel no longer cared at that point; he loves his sister enough to get revenge for her that she didn't even want.
Dipper giving up his hard fought time travel assisted friendship boost with Wendy, so Mabel can keep her new pig, Waddles. The thank-you hug she gave him afterwards was nothing short of adorable.
"That'll do, pig. That'll do."
Hell, even the intro of Gravity Falls introducing Mabel cuddling a pig is this.
"Did you hear that? She called me one of her boys!"
Mabel helping Grunkle Stan get over his fear of heights was both hilarious and adorable.
Just about every time Grunkle Stan decides to bond with his great niece and nephew.
Dipper sticking a bandaid on Mabel's skinned elbow in "Summerween".
In a somewhat creepy way, the Summerween Trickster being able to die happy in the knowledge that someone enjoyed eating him.
3 year old Dipper & Mabel dressed as kittens. D'awww...
When Mabel is sad that even after all that they didn't get any candy, Stan reveals the two bags left behind by those two kids from earlier.
The Lol Pigs segment during the credits gives a really warm fuzzy feeling to watch, especially since this was one of the freakiest and most intense episodes in the entire show.
Grunkle Stan trusts Mabel with the shack for 72 hours in "Boss Mabel". He does it to prove a point, however, its not often that Grunkle Stan acts are fueled by principle instead of money.
Some of Alex Hirsch'stweets make it clear how much he and his sister's childhood influenced the show. You can tell he put his heart into it!
Lance Bass appearing in the episode "Boyz Crazy" was a gift from Alex to Ariel, who was obsessed with the singer when she was younger.
The little interactions between Dipper and Mabel (grabbing her hand and leading her away from danger, pouring a soda for her at the table in Double Dipper, the high-fives, the affectionate punches, etc.) really enforce that they truly are the best of friends. It's sweet.
In "Carpet Diem", Dipper admits he misses spending time with Mabel and feels like he's getting left behind when she goes to hang out with her friends. That, plus the fact that they move back into the same room by the end of the episode, just shows how close they are and that they value each others' company more than anyone else's (which is arguably just about the sweetest thing in the world).
Dipper: Hey, um... Do you want to have a sleepover?
Mabel telling Grenda that she's too beautiful to need make-up, although probably intended as a joke given Grenda's "butch" appearance, is very sweet and genuine coming from Mabel.
In "Boyz Crazy", Dipper exposes Robby's song of having subliminal messages. Grunkle Stan states that he did the right thing and that until Wendy gets her life back together after dumping Robbie, the two of them could always go bowling together. There's also the scene where they give each other high-fives and the fact that Grunkle Stan knows what it's like for Dipper to lose someone he loves to music to be there to support him.
Somewhat Fridge-Heartwarming, but the fact that Stan cares enough about Wendy (his lazy, sarcastic employee who pelted him with water balloons for no reason two episodes prior) to actually believe Dipper's shenanigans and take a dangerous, off-road route to save her.
In the end, Mabel decides to let Sev'Ral Timez go and be free, even though she's still torn about how every guy she's met leaving her.
On a meta level: Series creator Alex Hirsch's sister Ariel had a huge crush on NSYNC's Lance Bass as a kid, so Alex cast Bass as a guest in this episode and invited Ariel to come meet him and get memorabilia signed. He also gave her a cameo in the episode. The code at the end of the episode reads HAPPY NOW, ARIEL?
In The Land Before Swine, Stan and Mabel making up after their fight, culminating in the two of them falling asleep together covered in tree sap.
Dipper and Soos also making up after their fight with their fist bump.
From "Dreamscaperers": The reason Stan acts so cold and bossy towards Dipper, and constantly making him do chores? He sees how weak he was when he was a young man in Dipper. Just like what his father did to him, Stan's toughening him up so he can become strong and proud.
He specifically says he does it so Dipper can fight back whatever the world throws at him. Considering all the danger in Gravity Falls (which Stan might already know about), it makes it even more heartwarming.
A minor one for the same episode comes from Bill Cipher. He may have pulled out that deer's teeth, but it was good to see that he actually bothered to restore the deer's teeth after he was done making his deal with Gideon.
In "Gideon Rises", Grunkle Stan being legitimately upset when he has to send Dipper and Mabel home because he can't take care of them, anymore. Even for all of the teasing and such, he really does love them.
At the end when Stan is considered a hero for exposing Gideon as a fraud to the whole town.
While affectionately noogie-ing Dipper and carrying Mabel on his shoulder, no less!
The montage at the Mystery Shack showed they were together again and that the Shack was finally theirs.
Special mention goes to Dipper and Mabel telling Stan about the journal, Soos water gunning them, and Mabel telling Dipper he was still a hero without the journal.
A subtle one is they kept calling the Mystery Shack their home.
Stan even has a framed photo of both Dipper and Mabel in the secret facility behind the candy machine.
Dipper and Wendy smiling at each other while they repair the Mystery Shack roof.
Dipper and Mabel desperately trying to hold on to each other as Gideon-bot picks them up.